LMFDB - Embedded newform 1710.2.d.e.1369.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1369,1710)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1710.1369");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1369.3
Root			$0.403032 + 0.403032i$ of defining polynomial
Character	$\chi$	$=$	1710.1369
Dual form			1710.2.d.e.1369.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(1.48119 + 1.67513i) q^{5} +3.35026i q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.48119 + 1.67513i) q^{5} +3.35026i q^{7} +1.00000i q^{8} +(1.67513 - 1.48119i) q^{10} +1.61213 q^{11} +1.35026i q^{13} +3.35026 q^{14} +1.00000 q^{16} -6.96239i q^{17} +1.00000 q^{19} +(-1.48119 - 1.67513i) q^{20} -1.61213i q^{22} -1.35026i q^{23} +(-0.612127 + 4.96239i) q^{25} +1.35026 q^{26} -3.35026i q^{28} +3.61213 q^{29} -2.31265 q^{31} -1.00000i q^{32} -6.96239 q^{34} +(-5.61213 + 4.96239i) q^{35} +11.2750i q^{37} -1.00000i q^{38} +(-1.67513 + 1.48119i) q^{40} +3.35026 q^{41} +10.3127i q^{43} -1.61213 q^{44} -1.35026 q^{46} +4.57452i q^{47} -4.22425 q^{49} +(4.96239 + 0.612127i) q^{50} -1.35026i q^{52} +11.9248i q^{53} +(2.38787 + 2.70052i) q^{55} -3.35026 q^{56} -3.61213i q^{58} +1.03761 q^{59} +2.00000 q^{61} +2.31265i q^{62} -1.00000 q^{64} +(-2.26187 + 2.00000i) q^{65} -9.92478i q^{67} +6.96239i q^{68} +(4.96239 + 5.61213i) q^{70} +0.775746 q^{71} +3.22425i q^{73} +11.2750 q^{74} -1.00000 q^{76} +5.40105i q^{77} -14.3127 q^{79} +(1.48119 + 1.67513i) q^{80} -3.35026i q^{82} +10.8872i q^{83} +(11.6629 - 10.3127i) q^{85} +10.3127 q^{86} +1.61213i q^{88} -2.57452 q^{89} -4.52373 q^{91} +1.35026i q^{92} +4.57452 q^{94} +(1.48119 + 1.67513i) q^{95} -1.16362i q^{97} +4.22425i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 2 q^{5}+O(q^{10}) $ 6 * q - 6 * q^4 - 2 * q^5	$ 6 q - 6 q^{4} - 2 q^{5} + 8 q^{11} + 6 q^{16} + 6 q^{19} + 2 q^{20} - 2 q^{25} - 12 q^{26} + 20 q^{29} + 28 q^{31} - 20 q^{34} - 32 q^{35} - 8 q^{44} + 12 q^{46} - 22 q^{49} + 8 q^{50} + 16 q^{55} + 28 q^{59} + 12 q^{61} - 6 q^{64} - 32 q^{65} + 8 q^{70} + 8 q^{71} + 4 q^{74} - 6 q^{76} - 44 q^{79} - 2 q^{80} + 8 q^{85} + 20 q^{86} + 8 q^{89} - 64 q^{91} + 4 q^{94} - 2 q^{95}+O(q^{100}) $ 6 * q - 6 * q^4 - 2 * q^5 + 8 * q^11 + 6 * q^16 + 6 * q^19 + 2 * q^20 - 2 * q^25 - 12 * q^26 + 20 * q^29 + 28 * q^31 - 20 * q^34 - 32 * q^35 - 8 * q^44 + 12 * q^46 - 22 * q^49 + 8 * q^50 + 16 * q^55 + 28 * q^59 + 12 * q^61 - 6 * q^64 - 32 * q^65 + 8 * q^70 + 8 * q^71 + 4 * q^74 - 6 * q^76 - 44 * q^79 - 2 * q^80 + 8 * q^85 + 20 * q^86 + 8 * q^89 - 64 * q^91 + 4 * q^94 - 2 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	1.48119	+	1.67513i	0.662410	+	0.749141i
$5$	1.48119	+	1.67513i	0.662410	+	0.749141i
$6$		0			0
$7$			3.35026i			1.26628i	0.774037	+	0.633140i	$0.218234\pi$
$7$			3.35026i			1.26628i	−0.774037	+	0.633140i	$0.781766\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	1.67513	−	1.48119i	0.529723	−	0.468395i
$11$	1.61213			0.486075			0.243037	−	0.970017i	$-0.421856\pi$
$11$	1.61213			0.486075			0.243037	+	0.970017i	$0.421856\pi$
$12$		0			0
$13$			1.35026i			0.374495i	0.982313	+	0.187248i	$0.0599567\pi$
$13$			1.35026i			0.374495i	−0.982313	+	0.187248i	$0.940043\pi$
$14$	3.35026			0.895395
$15$		0			0
$16$	1.00000			0.250000
$17$		−	6.96239i		−	1.68863i	−0.535849	−	0.844314i	$-0.680008\pi$
$17$		−	6.96239i		−	1.68863i	0.535849	−	0.844314i	$-0.319992\pi$
$18$		0			0
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−1.48119	−	1.67513i	−0.331205	−	0.374571i
$21$		0			0
$22$		−	1.61213i		−	0.343707i
$23$		−	1.35026i		−	0.281549i	−0.990042	−	0.140775i	$-0.955041\pi$
$23$		−	1.35026i		−	0.281549i	0.990042	−	0.140775i	$-0.0449593\pi$
$24$		0			0
$25$	−0.612127	+	4.96239i	−0.122425	+	0.992478i
$26$	1.35026			0.264808
$27$		0			0
$28$		−	3.35026i		−	0.633140i
$29$	3.61213			0.670755			0.335378	−	0.942084i	$-0.391136\pi$
$29$	3.61213			0.670755			0.335378	+	0.942084i	$0.391136\pi$
$30$		0			0
$31$	−2.31265			−0.415364			−0.207682	−	0.978196i	$-0.566592\pi$
$31$	−2.31265			−0.415364			−0.207682	+	0.978196i	$0.566592\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−6.96239			−1.19404
$35$	−5.61213	+	4.96239i	−0.948623	+	0.838797i
$36$		0			0
$37$			11.2750i			1.85360i	0.375549	+	0.926802i	$0.377454\pi$
$37$			11.2750i			1.85360i	−0.375549	+	0.926802i	$0.622546\pi$
$38$		−	1.00000i		−	0.162221i
$39$		0			0
$40$	−1.67513	+	1.48119i	−0.264861	+	0.234197i
$41$	3.35026			0.523223			0.261611	−	0.965173i	$-0.415746\pi$
$41$	3.35026			0.523223			0.261611	+	0.965173i	$0.415746\pi$
$42$		0			0
$43$			10.3127i			1.57266i	0.617804	+	0.786332i	$0.288023\pi$
$43$			10.3127i			1.57266i	−0.617804	+	0.786332i	$0.711977\pi$
$44$	−1.61213			−0.243037
$45$		0			0
$46$	−1.35026			−0.199085
$47$			4.57452i			0.667262i	0.942704	+	0.333631i	$0.108274\pi$
$47$			4.57452i			0.667262i	−0.942704	+	0.333631i	$0.891726\pi$
$48$		0			0
$49$	−4.22425			−0.603465
$50$	4.96239	+	0.612127i	0.701788	+	0.0865678i
$51$		0			0
$52$		−	1.35026i		−	0.187248i
$53$			11.9248i			1.63799i	0.573798	+	0.818997i	$0.305470\pi$
$53$			11.9248i			1.63799i	−0.573798	+	0.818997i	$0.694530\pi$
$54$		0			0
$55$	2.38787	+	2.70052i	0.321981	+	0.364139i
$56$	−3.35026			−0.447698
$57$		0			0
$58$		−	3.61213i		−	0.474295i
$59$	1.03761			0.135085			0.0675427	−	0.997716i	$-0.478484\pi$
$59$	1.03761			0.135085			0.0675427	+	0.997716i	$0.478484\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$			2.31265i			0.293707i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−2.26187	+	2.00000i	−0.280550	+	0.248069i
$66$		0			0
$67$		−	9.92478i		−	1.21250i	−0.795272	−	0.606252i	$-0.792672\pi$
$67$		−	9.92478i		−	1.21250i	0.795272	−	0.606252i	$-0.207328\pi$
$68$			6.96239i			0.844314i
$69$		0			0
$70$	4.96239	+	5.61213i	0.593119	+	0.670777i
$71$	0.775746			0.0920641			0.0460321	−	0.998940i	$-0.485342\pi$
$71$	0.775746			0.0920641			0.0460321	+	0.998940i	$0.485342\pi$
$72$		0			0
$73$			3.22425i			0.377370i	0.982038	+	0.188685i	$0.0604226\pi$
$73$			3.22425i			0.377370i	−0.982038	+	0.188685i	$0.939577\pi$
$74$	11.2750			1.31070
$75$		0			0
$76$	−1.00000			−0.114708
$77$			5.40105i			0.615506i
$78$		0			0
$79$	−14.3127			−1.61030			−0.805149	−	0.593072i	$-0.797915\pi$
$79$	−14.3127			−1.61030			−0.805149	+	0.593072i	$0.797915\pi$
$80$	1.48119	+	1.67513i	0.165603	+	0.187285i
$81$		0			0
$82$		−	3.35026i		−	0.369975i
$83$			10.8872i			1.19502i	0.801861	+	0.597511i	$0.203844\pi$
$83$			10.8872i			1.19502i	−0.801861	+	0.597511i	$0.796156\pi$
$84$		0			0
$85$	11.6629	−	10.3127i	1.26502	−	1.11856i
$86$	10.3127			1.11204
$87$		0			0
$88$			1.61213i			0.171853i
$89$	−2.57452			−0.272898			−0.136449	−	0.990647i	$-0.543569\pi$
$89$	−2.57452			−0.272898			−0.136449	+	0.990647i	$0.543569\pi$
$90$		0			0
$91$	−4.52373			−0.474216
$92$			1.35026i			0.140775i
$93$		0			0
$94$	4.57452			0.471825
$95$	1.48119	+	1.67513i	0.151967	+	0.171865i
$96$		0			0
$97$		−	1.16362i		−	0.118148i	−0.998254	−	0.0590738i	$-0.981185\pi$
$97$		−	1.16362i		−	0.118148i	0.998254	−	0.0590738i	$-0.0188147\pi$
$98$			4.22425i			0.426714i
$99$		0			0
$100$	0.612127	−	4.96239i	0.0612127	−	0.496239i
$101$	−8.88717			−0.884306			−0.442153	−	0.896940i	$-0.645785\pi$
$101$	−8.88717			−0.884306			−0.442153	+	0.896940i	$0.645785\pi$
$102$		0			0
$103$			7.03761i			0.693436i	0.937969	+	0.346718i	$0.112704\pi$
$103$			7.03761i			0.693436i	−0.937969	+	0.346718i	$0.887296\pi$
$104$	−1.35026			−0.132404
$105$		0			0
$106$	11.9248			1.15824
$107$		−	0.775746i		−	0.0749942i	−0.999297	−	0.0374971i	$-0.988062\pi$
$107$		−	0.775746i		−	0.0749942i	0.999297	−	0.0374971i	$-0.0119385\pi$
$108$		0			0
$109$	20.1622			1.93119			0.965594	−	0.260052i	$-0.0837399\pi$
$109$	20.1622			1.93119			0.965594	+	0.260052i	$0.0837399\pi$
$110$	2.70052	−	2.38787i	0.257485	−	0.227675i
$111$		0			0
$112$			3.35026i			0.316570i
$113$		−	11.1490i		−	1.04881i	−0.851468	−	0.524406i	$-0.824287\pi$
$113$		−	11.1490i		−	1.04881i	0.851468	−	0.524406i	$-0.175713\pi$
$114$		0			0
$115$	2.26187	−	2.00000i	0.210920	−	0.186501i
$116$	−3.61213			−0.335378
$117$		0			0
$118$		−	1.03761i		−	0.0955199i
$119$	23.3258			2.13827
$120$		0			0
$121$	−8.40105			−0.763732
$122$		−	2.00000i		−	0.181071i
$123$		0			0
$124$	2.31265			0.207682
$125$	−9.21933	+	6.32487i	−0.824602	+	0.565713i
$126$		0			0
$127$		−	13.7381i		−	1.21906i	−0.792762	−	0.609531i	$-0.791358\pi$
$127$		−	13.7381i		−	1.21906i	0.792762	−	0.609531i	$-0.208642\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	2.00000	+	2.26187i	0.175412	+	0.198379i
$131$	−5.61213			−0.490334			−0.245167	−	0.969481i	$-0.578843\pi$
$131$	−5.61213			−0.490334			−0.245167	+	0.969481i	$0.578843\pi$
$132$		0			0
$133$			3.35026i			0.290505i
$134$	−9.92478			−0.857370
$135$		0			0
$136$	6.96239			0.597020
$137$		−	17.6629i		−	1.50904i	−0.656275	−	0.754522i	$-0.727869\pi$
$137$		−	17.6629i		−	1.50904i	0.656275	−	0.754522i	$-0.272131\pi$
$138$		0			0
$139$	−10.7005			−0.907607			−0.453803	−	0.891102i	$-0.649933\pi$
$139$	−10.7005			−0.907607			−0.453803	+	0.891102i	$0.649933\pi$
$140$	5.61213	−	4.96239i	0.474311	−	0.419398i
$141$		0			0
$142$		−	0.775746i		−	0.0650992i
$143$			2.17679i			0.182033i
$144$		0			0
$145$	5.35026	+	6.05079i	0.444315	+	0.502490i
$146$	3.22425			0.266841
$147$		0			0
$148$		−	11.2750i		−	0.926802i
$149$	1.03761			0.0850044			0.0425022	−	0.999096i	$-0.486467\pi$
$149$	1.03761			0.0850044			0.0425022	+	0.999096i	$0.486467\pi$
$150$		0			0
$151$	1.16362			0.0946940			0.0473470	−	0.998879i	$-0.484923\pi$
$151$	1.16362			0.0946940			0.0473470	+	0.998879i	$0.484923\pi$
$152$			1.00000i			0.0811107i
$153$		0			0
$154$	5.40105			0.435229
$155$	−3.42548	−	3.87399i	−0.275142	−	0.311167i
$156$		0			0
$157$		−	10.9624i		−	0.874894i	−0.899244	−	0.437447i	$-0.855883\pi$
$157$		−	10.9624i		−	0.874894i	0.899244	−	0.437447i	$-0.144117\pi$
$158$			14.3127i			1.13865i
$159$		0			0
$160$	1.67513	−	1.48119i	0.132431	−	0.117099i
$161$	4.52373			0.356520
$162$		0			0
$163$			21.0132i			1.64588i	0.568129	+	0.822939i	$0.307667\pi$
$163$			21.0132i			1.64588i	−0.568129	+	0.822939i	$0.692333\pi$
$164$	−3.35026			−0.261611
$165$		0			0
$166$	10.8872			0.845008
$167$			9.92478i			0.768002i	0.923333	+	0.384001i	$0.125454\pi$
$167$			9.92478i			0.768002i	−0.923333	+	0.384001i	$0.874546\pi$
$168$		0			0
$169$	11.1768			0.859753
$170$	−10.3127	−	11.6629i	−0.790944	−	0.894505i
$171$		0			0
$172$		−	10.3127i		−	0.786332i
$173$		−	14.6253i		−	1.11194i	−0.831202	−	0.555971i	$-0.812347\pi$
$173$		−	14.6253i		−	1.11194i	0.831202	−	0.555971i	$-0.187653\pi$
$174$		0			0
$175$	−16.6253	−	2.05079i	−1.25675	−	0.155025i
$176$	1.61213			0.121519
$177$		0			0
$178$			2.57452i			0.192968i
$179$	11.7381			0.877349			0.438675	−	0.898646i	$-0.355448\pi$
$179$	11.7381			0.877349			0.438675	+	0.898646i	$0.355448\pi$
$180$		0			0
$181$	21.4617			1.59523			0.797617	−	0.603164i	$-0.206094\pi$
$181$	21.4617			1.59523			0.797617	+	0.603164i	$0.206094\pi$
$182$			4.52373i			0.335321i
$183$		0			0
$184$	1.35026			0.0995426
$185$	−18.8872	+	16.7005i	−1.38861	+	1.22785i
$186$		0			0
$187$		−	11.2243i		−	0.820799i
$188$		−	4.57452i		−	0.333631i
$189$		0			0
$190$	1.67513	−	1.48119i	0.121527	−	0.107457i
$191$	21.2750			1.53941			0.769704	−	0.638401i	$-0.220404\pi$
$191$	21.2750			1.53941			0.769704	+	0.638401i	$0.220404\pi$
$192$		0			0
$193$		−	14.1622i		−	1.01942i	−0.860347	−	0.509709i	$-0.829753\pi$
$193$		−	14.1622i		−	1.01942i	0.860347	−	0.509709i	$-0.170247\pi$
$194$	−1.16362			−0.0835430
$195$		0			0
$196$	4.22425			0.301732
$197$			3.87399i			0.276011i	0.990431	+	0.138005i	$0.0440691\pi$
$197$			3.87399i			0.276011i	−0.990431	+	0.138005i	$0.955931\pi$
$198$		0			0
$199$	−3.47627			−0.246426			−0.123213	−	0.992380i	$-0.539320\pi$
$199$	−3.47627			−0.246426			−0.123213	+	0.992380i	$0.539320\pi$
$200$	−4.96239	−	0.612127i	−0.350894	−	0.0432839i
$201$		0			0
$202$			8.88717i			0.625299i
$203$			12.1016i			0.849364i
$204$		0			0
$205$	4.96239	+	5.61213i	0.346588	+	0.391968i
$206$	7.03761			0.490334
$207$		0			0
$208$			1.35026i			0.0936238i
$209$	1.61213			0.111513
$210$		0			0
$211$	9.92478			0.683250			0.341625	−	0.939836i	$-0.389023\pi$
$211$	9.92478			0.683250			0.341625	+	0.939836i	$0.389023\pi$
$212$		−	11.9248i		−	0.818997i
$213$		0			0
$214$	−0.775746			−0.0530289
$215$	−17.2750	+	15.2750i	−1.17815	+	1.04175i
$216$		0			0
$217$		−	7.74798i		−	0.525967i
$218$		−	20.1622i		−	1.36556i
$219$		0			0
$220$	−2.38787	−	2.70052i	−0.160990	−	0.182069i
$221$	9.40105			0.632383
$222$		0			0
$223$			7.03761i			0.471273i	0.971841	+	0.235637i	$0.0757175\pi$
$223$			7.03761i			0.471273i	−0.971841	+	0.235637i	$0.924282\pi$
$224$	3.35026			0.223849
$225$		0			0
$226$	−11.1490			−0.741623
$227$		−	14.5501i		−	0.965723i	−0.875697	−	0.482861i	$-0.839598\pi$
$227$		−	14.5501i		−	0.965723i	0.875697	−	0.482861i	$-0.160402\pi$
$228$		0			0
$229$	−11.4010			−0.753402			−0.376701	−	0.926335i	$-0.622942\pi$
$229$	−11.4010			−0.753402			−0.376701	+	0.926335i	$0.622942\pi$
$230$	−2.00000	−	2.26187i	−0.131876	−	0.149143i
$231$		0			0
$232$			3.61213i			0.237148i
$233$		−	21.9149i		−	1.43569i	−0.696201	−	0.717847i	$-0.745128\pi$
$233$		−	21.9149i		−	1.43569i	0.696201	−	0.717847i	$-0.254872\pi$
$234$		0			0
$235$	−7.66291	+	6.77575i	−0.499873	+	0.442001i
$236$	−1.03761			−0.0675427
$237$		0			0
$238$		−	23.3258i		−	1.51199i
$239$	−13.2750			−0.858691			−0.429345	−	0.903140i	$-0.641256\pi$
$239$	−13.2750			−0.858691			−0.429345	+	0.903140i	$0.641256\pi$
$240$		0			0
$241$	21.3258			1.37372			0.686859	−	0.726791i	$-0.258989\pi$
$241$	21.3258			1.37372			0.686859	+	0.726791i	$0.258989\pi$
$242$			8.40105i			0.540040i
$243$		0			0
$244$	−2.00000			−0.128037
$245$	−6.25694	−	7.07618i	−0.399741	−	0.452080i
$246$		0			0
$247$			1.35026i			0.0859151i
$248$		−	2.31265i		−	0.146853i
$249$		0			0
$250$	6.32487	+	9.21933i	0.400020	+	0.583082i
$251$	−16.3127			−1.02965			−0.514823	−	0.857297i	$-0.672142\pi$
$251$	−16.3127			−1.02965			−0.514823	+	0.857297i	$0.672142\pi$
$252$		0			0
$253$		−	2.17679i		−	0.136854i
$254$	−13.7381			−0.862007
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	24.5501i		−	1.53139i	−0.643203	−	0.765696i	$-0.722395\pi$
$257$		−	24.5501i		−	1.53139i	0.643203	−	0.765696i	$-0.277605\pi$
$258$		0			0
$259$	−37.7743			−2.34718
$260$	2.26187	−	2.00000i	0.140275	−	0.124035i
$261$		0			0
$262$			5.61213i			0.346718i
$263$			30.3488i			1.87139i	0.352810	+	0.935695i	$0.385226\pi$
$263$			30.3488i			1.87139i	−0.352810	+	0.935695i	$0.614774\pi$
$264$		0			0
$265$	−19.9756	+	17.6629i	−1.22709	+	1.08502i
$266$	3.35026			0.205418
$267$		0			0
$268$			9.92478i			0.606252i
$269$	14.3127			0.872658			0.436329	−	0.899787i	$-0.356278\pi$
$269$	14.3127			0.872658			0.436329	+	0.899787i	$0.356278\pi$
$270$		0			0
$271$	−7.32582			−0.445012			−0.222506	−	0.974931i	$-0.571424\pi$
$271$	−7.32582			−0.445012			−0.222506	+	0.974931i	$0.571424\pi$
$272$		−	6.96239i		−	0.422157i
$273$		0			0
$274$	−17.6629			−1.06706
$275$	−0.986826	+	8.00000i	−0.0595079	+	0.482418i
$276$		0			0
$277$		−	14.4387i		−	0.867535i	−0.901025	−	0.433767i	$-0.857184\pi$
$277$		−	14.4387i		−	0.867535i	0.901025	−	0.433767i	$-0.142816\pi$
$278$			10.7005i			0.641775i
$279$		0			0
$280$	−4.96239	−	5.61213i	−0.296559	−	0.335389i
$281$	11.9756			0.714402			0.357201	−	0.934028i	$-0.383731\pi$
$281$	11.9756			0.714402			0.357201	+	0.934028i	$0.383731\pi$
$282$		0			0
$283$			24.4894i			1.45575i	0.685712	+	0.727873i	$0.259491\pi$
$283$			24.4894i			1.45575i	−0.685712	+	0.727873i	$0.740509\pi$
$284$	−0.775746			−0.0460321
$285$		0			0
$286$	2.17679			0.128716
$287$			11.2243i			0.662547i
$288$		0			0
$289$	−31.4749			−1.85146
$290$	6.05079	−	5.35026i	0.355314	−	0.314178i
$291$		0			0
$292$		−	3.22425i		−	0.188685i
$293$		−	18.1016i		−	1.05751i	−0.848776	−	0.528753i	$-0.822660\pi$
$293$		−	18.1016i		−	1.05751i	0.848776	−	0.528753i	$-0.177340\pi$
$294$		0			0
$295$	1.53690	+	1.73813i	0.0894820	+	0.101198i
$296$	−11.2750			−0.655348
$297$		0			0
$298$		−	1.03761i		−	0.0601072i
$299$	1.82321			0.105439
$300$		0			0
$301$	−34.5501			−1.99143
$302$		−	1.16362i		−	0.0669588i
$303$		0			0
$304$	1.00000			0.0573539
$305$	2.96239	+	3.35026i	0.169626	+	0.191835i
$306$		0			0
$307$		−	29.9248i		−	1.70790i	−0.520357	−	0.853949i	$-0.674201\pi$
$307$		−	29.9248i		−	1.70790i	0.520357	−	0.853949i	$-0.325799\pi$
$308$		−	5.40105i		−	0.307753i
$309$		0			0
$310$	−3.87399	+	3.42548i	−0.220028	+	0.194554i
$311$	21.2750			1.20640			0.603198	−	0.797591i	$-0.293893\pi$
$311$	21.2750			1.20640			0.603198	+	0.797591i	$0.293893\pi$
$312$		0			0
$313$			17.4010i			0.983565i	0.870718	+	0.491783i	$0.163655\pi$
$313$			17.4010i			0.983565i	−0.870718	+	0.491783i	$0.836345\pi$
$314$	−10.9624			−0.618643
$315$		0			0
$316$	14.3127			0.805149
$317$			14.1016i			0.792023i	0.918246	+	0.396012i	$0.129606\pi$
$317$			14.1016i			0.792023i	−0.918246	+	0.396012i	$0.870394\pi$
$318$		0			0
$319$	5.82321			0.326037
$320$	−1.48119	−	1.67513i	−0.0828013	−	0.0936427i
$321$		0			0
$322$		−	4.52373i		−	0.252098i
$323$		−	6.96239i		−	0.387398i
$324$		0			0
$325$	−6.70052	−	0.826531i	−0.371678	−	0.0458477i
$326$	21.0132			1.16381
$327$		0			0
$328$			3.35026i			0.184987i
$329$	−15.3258			−0.844940
$330$		0			0
$331$	6.85097			0.376563			0.188282	−	0.982115i	$-0.439708\pi$
$331$	6.85097			0.376563			0.188282	+	0.982115i	$0.439708\pi$
$332$		−	10.8872i		−	0.597511i
$333$		0			0
$334$	9.92478			0.543060
$335$	16.6253	−	14.7005i	0.908337	−	0.803175i
$336$		0			0
$337$		−	24.2374i		−	1.32030i	−0.751135	−	0.660148i	$-0.770493\pi$
$337$		−	24.2374i		−	1.32030i	0.751135	−	0.660148i	$-0.229507\pi$
$338$		−	11.1768i		−	0.607937i
$339$		0			0
$340$	−11.6629	+	10.3127i	−0.632510	+	0.559282i
$341$	−3.72829			−0.201898
$342$		0			0
$343$			9.29948i			0.502125i
$344$	−10.3127			−0.556021
$345$		0			0
$346$	−14.6253			−0.786261
$347$			0.962389i			0.0516637i	0.999666	+	0.0258319i	$0.00822345\pi$
$347$			0.962389i			0.0516637i	−0.999666	+	0.0258319i	$0.991777\pi$
$348$		0			0
$349$	1.37470			0.0735860			0.0367930	−	0.999323i	$-0.488286\pi$
$349$	1.37470			0.0735860			0.0367930	+	0.999323i	$0.488286\pi$
$350$	−2.05079	+	16.6253i	−0.109619	+	0.888660i
$351$		0			0
$352$		−	1.61213i		−	0.0859267i
$353$		−	28.7367i		−	1.52950i	−0.644326	−	0.764751i	$-0.722862\pi$
$353$		−	28.7367i		−	1.52950i	0.644326	−	0.764751i	$-0.277138\pi$
$354$		0			0
$355$	1.14903	+	1.29948i	0.0609842	+	0.0689691i
$356$	2.57452			0.136449
$357$		0			0
$358$		−	11.7381i		−	0.620380i
$359$	31.1998			1.64666			0.823332	−	0.567561i	$-0.192113\pi$
$359$	31.1998			1.64666			0.823332	+	0.567561i	$0.192113\pi$
$360$		0			0
$361$	1.00000			0.0526316
$362$		−	21.4617i		−	1.12800i
$363$		0			0
$364$	4.52373			0.237108
$365$	−5.40105	+	4.77575i	−0.282704	+	0.249974i
$366$		0			0
$367$		−	20.1260i		−	1.05057i	−0.850927	−	0.525285i	$-0.823959\pi$
$367$		−	20.1260i		−	1.05057i	0.850927	−	0.525285i	$-0.176041\pi$
$368$		−	1.35026i		−	0.0703873i
$369$		0			0
$370$	16.7005	+	18.8872i	0.868219	+	0.981897i
$371$	−39.9511			−2.07416
$372$		0			0
$373$		−	17.9756i		−	0.930739i	−0.885116	−	0.465370i	$-0.845921\pi$
$373$		−	17.9756i		−	0.930739i	0.885116	−	0.465370i	$-0.154079\pi$
$374$	−11.2243			−0.580392
$375$		0			0
$376$	−4.57452			−0.235913
$377$			4.87732i			0.251195i
$378$		0			0
$379$	−1.67276			−0.0859240			−0.0429620	−	0.999077i	$-0.513679\pi$
$379$	−1.67276			−0.0859240			−0.0429620	+	0.999077i	$0.513679\pi$
$380$	−1.48119	−	1.67513i	−0.0759837	−	0.0859324i
$381$		0			0
$382$		−	21.2750i		−	1.08853i
$383$		−	31.8496i		−	1.62744i	−0.581260	−	0.813718i	$-0.697440\pi$
$383$		−	31.8496i		−	1.62744i	0.581260	−	0.813718i	$-0.302560\pi$
$384$		0			0
$385$	−9.04746	+	8.00000i	−0.461101	+	0.407718i
$386$	−14.1622			−0.720837
$387$		0			0
$388$			1.16362i			0.0590738i
$389$	−10.3371			−0.524111			−0.262056	−	0.965053i	$-0.584400\pi$
$389$	−10.3371			−0.524111			−0.262056	+	0.965053i	$0.584400\pi$
$390$		0			0
$391$	−9.40105			−0.475431
$392$		−	4.22425i		−	0.213357i
$393$		0			0
$394$	3.87399			0.195169
$395$	−21.1998	−	23.9756i	−1.06668	−	1.20634i
$396$		0			0
$397$			31.4372i			1.57779i	0.614528	+	0.788895i	$0.289346\pi$
$397$			31.4372i			1.57779i	−0.614528	+	0.788895i	$0.710654\pi$
$398$			3.47627i			0.174250i
$399$		0			0
$400$	−0.612127	+	4.96239i	−0.0306063	+	0.248119i
$401$	−5.94921			−0.297090			−0.148545	−	0.988906i	$-0.547459\pi$
$401$	−5.94921			−0.297090			−0.148545	+	0.988906i	$0.547459\pi$
$402$		0			0
$403$		−	3.12268i		−	0.155552i
$404$	8.88717			0.442153
$405$		0			0
$406$	12.1016			0.600591
$407$			18.1768i			0.900990i
$408$		0			0
$409$	30.9986			1.53278			0.766391	−	0.642375i	$-0.222051\pi$
$409$	30.9986			1.53278			0.766391	+	0.642375i	$0.222051\pi$
$410$	5.61213	−	4.96239i	0.277163	−	0.245075i
$411$		0			0
$412$		−	7.03761i		−	0.346718i
$413$			3.47627i			0.171056i
$414$		0			0
$415$	−18.2374	+	16.1260i	−0.895240	+	0.791595i
$416$	1.35026			0.0662020
$417$		0			0
$418$		−	1.61213i		−	0.0788517i
$419$	−34.3390			−1.67757			−0.838785	−	0.544463i	$-0.816734\pi$
$419$	−34.3390			−1.67757			−0.838785	+	0.544463i	$0.816734\pi$
$420$		0			0
$421$	22.8627			1.11426			0.557131	−	0.830425i	$-0.311902\pi$
$421$	22.8627			1.11426			0.557131	+	0.830425i	$0.311902\pi$
$422$		−	9.92478i		−	0.483131i
$423$		0			0
$424$	−11.9248			−0.579118
$425$	34.5501	+	4.26187i	1.67592	+	0.206731i
$426$		0			0
$427$			6.70052i			0.324261i
$428$			0.775746i			0.0374971i
$429$		0			0
$430$	15.2750	+	17.2750i	0.736628	+	0.833076i
$431$	−11.5975			−0.558634			−0.279317	−	0.960199i	$-0.590108\pi$
$431$	−11.5975			−0.558634			−0.279317	+	0.960199i	$0.590108\pi$
$432$		0			0
$433$			27.8350i			1.33766i	0.743414	+	0.668832i	$0.233205\pi$
$433$			27.8350i			1.33766i	−0.743414	+	0.668832i	$0.766795\pi$
$434$	−7.74798			−0.371915
$435$		0			0
$436$	−20.1622			−0.965594
$437$		−	1.35026i		−	0.0645918i
$438$		0			0
$439$	38.7875			1.85123			0.925613	−	0.378471i	$-0.123550\pi$
$439$	38.7875			1.85123			0.925613	+	0.378471i	$0.123550\pi$
$440$	−2.70052	+	2.38787i	−0.128742	+	0.113837i
$441$		0			0
$442$		−	9.40105i		−	0.447162i
$443$			29.2144i			1.38802i	0.719966	+	0.694009i	$0.244157\pi$
$443$			29.2144i			1.38802i	−0.719966	+	0.694009i	$0.755843\pi$
$444$		0			0
$445$	−3.81336	−	4.31265i	−0.180770	−	0.204439i
$446$	7.03761			0.333241
$447$		0			0
$448$		−	3.35026i		−	0.158285i
$449$	−20.4993			−0.967421			−0.483711	−	0.875228i	$-0.660711\pi$
$449$	−20.4993			−0.967421			−0.483711	+	0.875228i	$0.660711\pi$
$450$		0			0
$451$	5.40105			0.254325
$452$			11.1490i			0.524406i
$453$		0			0
$454$	−14.5501			−0.682869
$455$	−6.70052	−	7.57784i	−0.314125	−	0.355255i
$456$		0			0
$457$		−	6.44851i		−	0.301648i	−0.988561	−	0.150824i	$-0.951807\pi$
$457$		−	6.44851i		−	0.301648i	0.988561	−	0.150824i	$-0.0481927\pi$
$458$			11.4010i			0.532736i
$459$		0			0
$460$	−2.26187	+	2.00000i	−0.105460	+	0.0932505i
$461$	13.5125			0.629338			0.314669	−	0.949201i	$-0.398106\pi$
$461$	13.5125			0.629338			0.314669	+	0.949201i	$0.398106\pi$
$462$		0			0
$463$			6.20123i			0.288196i	0.989563	+	0.144098i	$0.0460280\pi$
$463$			6.20123i			0.288196i	−0.989563	+	0.144098i	$0.953972\pi$
$464$	3.61213			0.167689
$465$		0			0
$466$	−21.9149			−1.01519
$467$		−	16.5599i		−	0.766302i	−0.923686	−	0.383151i	$-0.874839\pi$
$467$		−	16.5599i		−	0.766302i	0.923686	−	0.383151i	$-0.125161\pi$
$468$		0			0
$469$	33.2506			1.53537
$470$	6.77575	+	7.66291i	0.312542	+	0.353464i
$471$		0			0
$472$			1.03761i			0.0477599i
$473$			16.6253i			0.764432i
$474$		0			0
$475$	−0.612127	+	4.96239i	−0.0280863	+	0.227690i
$476$	−23.3258			−1.06914
$477$		0			0
$478$			13.2750i			0.607186i
$479$	−30.5256			−1.39475			−0.697376	−	0.716705i	$-0.745649\pi$
$479$	−30.5256			−1.39475			−0.697376	+	0.716705i	$0.745649\pi$
$480$		0			0
$481$	−15.2243			−0.694166
$482$		−	21.3258i		−	0.971365i
$483$		0			0
$484$	8.40105			0.381866
$485$	1.94921	−	1.72355i	0.0885093	−	0.0782622i
$486$		0			0
$487$			2.51388i			0.113915i	0.998377	+	0.0569574i	$0.0181399\pi$
$487$			2.51388i			0.113915i	−0.998377	+	0.0569574i	$0.981860\pi$
$488$			2.00000i			0.0905357i
$489$		0			0
$490$	−7.07618	+	6.25694i	−0.319669	+	0.282660i
$491$	−1.46168			−0.0659648			−0.0329824	−	0.999456i	$-0.510501\pi$
$491$	−1.46168			−0.0659648			−0.0329824	+	0.999456i	$0.510501\pi$
$492$		0			0
$493$		−	25.1490i		−	1.13266i
$494$	1.35026			0.0607511
$495$		0			0
$496$	−2.31265			−0.103841
$497$			2.59895i			0.116579i
$498$		0			0
$499$	5.55149			0.248519			0.124259	−	0.992250i	$-0.460344\pi$
$499$	5.55149			0.248519			0.124259	+	0.992250i	$0.460344\pi$
$500$	9.21933	−	6.32487i	0.412301	−	0.282857i
$501$		0			0
$502$			16.3127i			0.728069i
$503$		−	6.90175i		−	0.307734i	−0.988092	−	0.153867i	$-0.950827\pi$
$503$		−	6.90175i		−	0.307734i	0.988092	−	0.153867i	$-0.0491727\pi$
$504$		0			0
$505$	−13.1636	−	14.8872i	−0.585773	−	0.662470i
$506$	−2.17679			−0.0967703
$507$		0			0
$508$			13.7381i			0.609531i
$509$	8.76116			0.388331			0.194166	−	0.980969i	$-0.437800\pi$
$509$	8.76116			0.388331			0.194166	+	0.980969i	$0.437800\pi$
$510$		0			0
$511$	−10.8021			−0.477857
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−24.5501			−1.08286
$515$	−11.7889	+	10.4241i	−0.519482	+	0.459339i
$516$		0			0
$517$			7.37470i			0.324339i
$518$			37.7743i			1.65971i
$519$		0			0
$520$	−2.00000	−	2.26187i	−0.0877058	−	0.0991893i
$521$	−39.4518			−1.72842			−0.864208	−	0.503135i	$-0.832180\pi$
$521$	−39.4518			−1.72842			−0.864208	+	0.503135i	$0.832180\pi$
$522$		0			0
$523$		−	37.5026i		−	1.63987i	−0.572453	−	0.819937i	$-0.694008\pi$
$523$		−	37.5026i		−	1.63987i	0.572453	−	0.819937i	$-0.305992\pi$
$524$	5.61213			0.245167
$525$		0			0
$526$	30.3488			1.32327
$527$			16.1016i			0.701395i
$528$		0			0
$529$	21.1768			0.920730
$530$	17.6629	+	19.9756i	0.767228	+	0.867683i
$531$		0			0
$532$		−	3.35026i		−	0.145252i
$533$			4.52373i			0.195945i
$534$		0			0
$535$	1.29948	−	1.14903i	0.0561813	−	0.0496769i
$536$	9.92478			0.428685
$537$		0			0
$538$		−	14.3127i		−	0.617062i
$539$	−6.81003			−0.293329
$540$		0			0
$541$	−30.7757			−1.32315			−0.661576	−	0.749878i	$-0.730112\pi$
$541$	−30.7757			−1.32315			−0.661576	+	0.749878i	$0.730112\pi$
$542$			7.32582i			0.314671i
$543$		0			0
$544$	−6.96239			−0.298510
$545$	29.8641	+	33.7743i	1.27924	+	1.44673i
$546$		0			0
$547$			1.77433i			0.0758649i	0.999280	+	0.0379325i	$0.0120772\pi$
$547$			1.77433i			0.0758649i	−0.999280	+	0.0379325i	$0.987923\pi$
$548$			17.6629i			0.754522i
$549$		0			0
$550$	8.00000	+	0.986826i	0.341121	+	0.0420784i
$551$	3.61213			0.153882
$552$		0			0
$553$		−	47.9511i		−	2.03909i
$554$	−14.4387			−0.613440
$555$		0			0
$556$	10.7005			0.453803
$557$		−	8.90175i		−	0.377179i	−0.982056	−	0.188590i	$-0.939608\pi$
$557$		−	8.90175i		−	0.377179i	0.982056	−	0.188590i	$-0.0603916\pi$
$558$		0			0
$559$	−13.9248			−0.588955
$560$	−5.61213	+	4.96239i	−0.237156	+	0.209699i
$561$		0			0
$562$		−	11.9756i		−	0.505159i
$563$			10.9525i			0.461595i	0.973002	+	0.230797i	$0.0741334\pi$
$563$			10.9525i			0.461595i	−0.973002	+	0.230797i	$0.925867\pi$
$564$		0			0
$565$	18.6761	−	16.5139i	0.785709	−	0.694744i
$566$	24.4894			1.02937
$567$		0			0
$568$			0.775746i			0.0325496i
$569$	−10.2012			−0.427658			−0.213829	−	0.976871i	$-0.568594\pi$
$569$	−10.2012			−0.427658			−0.213829	+	0.976871i	$0.568594\pi$
$570$		0			0
$571$	−25.6531			−1.07355			−0.536774	−	0.843726i	$-0.680357\pi$
$571$	−25.6531			−1.07355			−0.536774	+	0.843726i	$0.680357\pi$
$572$		−	2.17679i		−	0.0910163i
$573$		0			0
$574$	11.2243			0.468491
$575$	6.70052	+	0.826531i	0.279431	+	0.0344687i
$576$		0			0
$577$		−	6.44851i		−	0.268455i	−0.990951	−	0.134227i	$-0.957145\pi$
$577$		−	6.44851i		−	0.268455i	0.990951	−	0.134227i	$-0.0428553\pi$
$578$			31.4749i			1.30918i
$579$		0			0
$580$	−5.35026	−	6.05079i	−0.222158	−	0.251245i
$581$	−36.4749			−1.51323
$582$		0			0
$583$			19.2243i			0.796187i
$584$	−3.22425			−0.133421
$585$		0			0
$586$	−18.1016			−0.747769
$587$		−	41.8397i		−	1.72691i	−0.504426	−	0.863455i	$-0.668296\pi$
$587$		−	41.8397i		−	1.72691i	0.504426	−	0.863455i	$-0.331704\pi$
$588$		0			0
$589$	−2.31265			−0.0952911
$590$	1.73813	−	1.53690i	0.0715579	−	0.0632733i
$591$		0			0
$592$			11.2750i			0.463401i
$593$		−	8.73672i		−	0.358774i	−0.983779	−	0.179387i	$-0.942589\pi$
$593$		−	8.73672i		−	0.358774i	0.983779	−	0.179387i	$-0.0574114\pi$
$594$		0			0
$595$	34.5501	+	39.0738i	1.41642	+	1.60187i
$596$	−1.03761			−0.0425022
$597$		0			0
$598$		−	1.82321i		−	0.0745565i
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	30.6253			1.24923			0.624616	−	0.780932i	$-0.285255\pi$
$601$	30.6253			1.24923			0.624616	+	0.780932i	$0.285255\pi$
$602$			34.5501i			1.40816i
$603$		0			0
$604$	−1.16362			−0.0473470
$605$	−12.4436	−	14.0729i	−0.505904	−	0.572143i
$606$		0			0
$607$			2.51388i			0.102035i	0.998698	+	0.0510176i	$0.0162465\pi$
$607$			2.51388i			0.102035i	−0.998698	+	0.0510176i	$0.983754\pi$
$608$		−	1.00000i		−	0.0405554i
$609$		0			0
$610$	3.35026	−	2.96239i	0.135648	−	0.119944i
$611$	−6.17679			−0.249886
$612$		0			0
$613$		−	2.96239i		−	0.119650i	−0.998209	−	0.0598249i	$-0.980946\pi$
$613$		−	2.96239i		−	0.119650i	0.998209	−	0.0598249i	$-0.0190542\pi$
$614$	−29.9248			−1.20767
$615$		0			0
$616$	−5.40105			−0.217614
$617$		−	18.3371i		−	0.738223i	−0.929385	−	0.369112i	$-0.879662\pi$
$617$		−	18.3371i		−	0.738223i	0.929385	−	0.369112i	$-0.120338\pi$
$618$		0			0
$619$	40.7269			1.63695			0.818476	−	0.574541i	$-0.194820\pi$
$619$	40.7269			1.63695			0.818476	+	0.574541i	$0.194820\pi$
$620$	3.42548	+	3.87399i	0.137571	+	0.155583i
$621$		0			0
$622$		−	21.2750i		−	0.853051i
$623$		−	8.62530i		−	0.345565i
$624$		0			0
$625$	−24.2506	−	6.07522i	−0.970024	−	0.243009i
$626$	17.4010			0.695486
$627$		0			0
$628$			10.9624i			0.437447i
$629$	78.5012			3.13005
$630$		0			0
$631$	−5.92478			−0.235862			−0.117931	−	0.993022i	$-0.537626\pi$
$631$	−5.92478			−0.235862			−0.117931	+	0.993022i	$0.537626\pi$
$632$		−	14.3127i		−	0.569327i
$633$		0			0
$634$	14.1016			0.560045
$635$	23.0132	−	20.3488i	0.913250	−	0.807519i
$636$		0			0
$637$		−	5.70385i		−	0.225995i
$638$		−	5.82321i		−	0.230543i
$639$		0			0
$640$	−1.67513	+	1.48119i	−0.0662154	+	0.0585493i
$641$	−19.0494			−0.752405			−0.376202	−	0.926537i	$-0.622770\pi$
$641$	−19.0494			−0.752405			−0.376202	+	0.926537i	$0.622770\pi$
$642$		0			0
$643$		−	1.06205i		−	0.0418831i	−0.999781	−	0.0209416i	$-0.993334\pi$
$643$		−	1.06205i		−	0.0418831i	0.999781	−	0.0209416i	$-0.00666639\pi$
$644$	−4.52373			−0.178260
$645$		0			0
$646$	−6.96239			−0.273932
$647$			26.6497i			1.04771i	0.851808	+	0.523855i	$0.175507\pi$
$647$			26.6497i			1.04771i	−0.851808	+	0.523855i	$0.824493\pi$
$648$		0			0
$649$	1.67276			0.0656616
$650$	−0.826531	+	6.70052i	−0.0324192	+	0.262816i
$651$		0			0
$652$		−	21.0132i		−	0.822939i
$653$			9.64832i			0.377568i	0.982019	+	0.188784i	$0.0604546\pi$
$653$			9.64832i			0.377568i	−0.982019	+	0.188784i	$0.939545\pi$
$654$		0			0
$655$	−8.31265	−	9.40105i	−0.324802	−	0.367329i
$656$	3.35026			0.130806
$657$		0			0
$658$			15.3258i			0.597463i
$659$	10.0654			0.392091			0.196046	−	0.980595i	$-0.437190\pi$
$659$	10.0654			0.392091			0.196046	+	0.980595i	$0.437190\pi$
$660$		0			0
$661$	13.5633			0.527549			0.263775	−	0.964584i	$-0.415032\pi$
$661$	13.5633			0.527549			0.263775	+	0.964584i	$0.415032\pi$
$662$		−	6.85097i		−	0.266270i
$663$		0			0
$664$	−10.8872			−0.422504
$665$	−5.61213	+	4.96239i	−0.217629	+	0.192433i
$666$		0			0
$667$		−	4.87732i		−	0.188850i
$668$		−	9.92478i		−	0.384001i
$669$		0			0
$670$	−14.7005	−	16.6253i	−0.567931	−	0.642291i
$671$	3.22425			0.124471
$672$		0			0
$673$		−	5.93937i		−	0.228946i	−0.993426	−	0.114473i	$-0.963482\pi$
$673$		−	5.93937i		−	0.228946i	0.993426	−	0.114473i	$-0.0365179\pi$
$674$	−24.2374			−0.933591
$675$		0			0
$676$	−11.1768			−0.429877
$677$		−	24.9525i		−	0.959004i	−0.877541	−	0.479502i	$-0.840817\pi$
$677$		−	24.9525i		−	0.959004i	0.877541	−	0.479502i	$-0.159183\pi$
$678$		0			0
$679$	3.89843			0.149608
$680$	10.3127	+	11.6629i	0.395472	+	0.447252i
$681$		0			0
$682$			3.72829i			0.142763i
$683$		−	45.6239i		−	1.74575i	−0.487944	−	0.872875i	$-0.662253\pi$
$683$		−	45.6239i		−	1.74575i	0.487944	−	0.872875i	$-0.337747\pi$
$684$		0			0
$685$	29.5877	−	26.1622i	1.13049	−	0.999606i
$686$	9.29948			0.355056
$687$		0			0
$688$			10.3127i			0.393166i
$689$	−16.1016			−0.613421
$690$		0			0
$691$	−11.7480			−0.446914			−0.223457	−	0.974714i	$-0.571734\pi$
$691$	−11.7480			−0.446914			−0.223457	+	0.974714i	$0.571734\pi$
$692$			14.6253i			0.555971i
$693$		0			0
$694$	0.962389			0.0365318
$695$	−15.8496	−	17.9248i	−0.601208	−	0.679926i
$696$		0			0
$697$		−	23.3258i		−	0.883529i
$698$		−	1.37470i		−	0.0520331i
$699$		0			0
$700$	16.6253	+	2.05079i	0.628377	+	0.0775124i
$701$	43.8105			1.65470			0.827350	−	0.561686i	$-0.189847\pi$
$701$	43.8105			1.65470			0.827350	+	0.561686i	$0.189847\pi$
$702$		0			0
$703$			11.2750i			0.425246i
$704$	−1.61213			−0.0607593
$705$		0			0
$706$	−28.7367			−1.08152
$707$		−	29.7743i		−	1.11978i
$708$		0			0
$709$	29.5975			1.11156			0.555779	−	0.831330i	$-0.312420\pi$
$709$	29.5975			1.11156			0.555779	+	0.831330i	$0.312420\pi$
$710$	1.29948	−	1.14903i	0.0487685	−	0.0431224i
$711$		0			0
$712$		−	2.57452i		−	0.0964840i
$713$			3.12268i			0.116945i
$714$		0			0
$715$	−3.64641	+	3.22425i	−0.136368	+	0.120580i
$716$	−11.7381			−0.438675
$717$		0			0
$718$		−	31.1998i		−	1.16437i
$719$	7.45183			0.277906			0.138953	−	0.990299i	$-0.455626\pi$
$719$	7.45183			0.277906			0.138953	+	0.990299i	$0.455626\pi$
$720$		0			0
$721$	−23.5778			−0.878085
$722$		−	1.00000i		−	0.0372161i
$723$		0			0
$724$	−21.4617			−0.797617
$725$	−2.21108	+	17.9248i	−0.0821174	+	0.665710i
$726$		0			0
$727$			0.600863i			0.0222848i	0.999938	+	0.0111424i	$0.00354681\pi$
$727$			0.600863i			0.0222848i	−0.999938	+	0.0111424i	$0.996453\pi$
$728$		−	4.52373i		−	0.167661i
$729$		0			0
$730$	4.77575	+	5.40105i	0.176758	+	0.199902i
$731$	71.8007			2.65564
$732$		0			0
$733$		−	36.0625i		−	1.33200i	−0.745952	−	0.666000i	$-0.768005\pi$
$733$		−	36.0625i		−	1.33200i	0.745952	−	0.666000i	$-0.231995\pi$
$734$	−20.1260			−0.742865
$735$		0			0
$736$	−1.35026			−0.0497713
$737$		−	16.0000i		−	0.589368i
$738$		0			0
$739$	14.1768			0.521502			0.260751	−	0.965406i	$-0.416030\pi$
$739$	14.1768			0.521502			0.260751	+	0.965406i	$0.416030\pi$
$740$	18.8872	−	16.7005i	0.694306	−	0.613923i
$741$		0			0
$742$			39.9511i			1.46665i
$743$			24.9986i			0.917109i	0.888666	+	0.458555i	$0.151633\pi$
$743$			24.9986i			0.917109i	−0.888666	+	0.458555i	$0.848367\pi$
$744$		0			0
$745$	1.53690	+	1.73813i	0.0563078	+	0.0636803i
$746$	−17.9756			−0.658132
$747$		0			0
$748$			11.2243i			0.410399i
$749$	2.59895			0.0949637
$750$		0			0
$751$	−10.2111			−0.372608			−0.186304	−	0.982492i	$-0.559651\pi$
$751$	−10.2111			−0.372608			−0.186304	+	0.982492i	$0.559651\pi$
$752$			4.57452i			0.166815i
$753$		0			0
$754$	4.87732			0.177621
$755$	1.72355	+	1.94921i	0.0627263	+	0.0709392i
$756$		0			0
$757$			44.4847i			1.61682i	0.588617	+	0.808412i	$0.299673\pi$
$757$			44.4847i			1.61682i	−0.588617	+	0.808412i	$0.700327\pi$
$758$			1.67276i			0.0607574i
$759$		0			0
$760$	−1.67513	+	1.48119i	−0.0607634	+	0.0537286i
$761$	−27.1490			−0.984152			−0.492076	−	0.870552i	$-0.663762\pi$
$761$	−27.1490			−0.984152			−0.492076	+	0.870552i	$0.663762\pi$
$762$		0			0
$763$			67.5487i			2.44543i
$764$	−21.2750			−0.769704
$765$		0			0
$766$	−31.8496			−1.15077
$767$			1.40105i			0.0505889i
$768$		0			0
$769$	31.4010			1.13235			0.566175	−	0.824285i	$-0.308422\pi$
$769$	31.4010			1.13235			0.566175	+	0.824285i	$0.308422\pi$
$770$	8.00000	+	9.04746i	0.288300	+	0.326048i
$771$		0			0
$772$			14.1622i			0.509709i
$773$			4.02635i			0.144818i	0.997375	+	0.0724088i	$0.0230686\pi$
$773$			4.02635i			0.144818i	−0.997375	+	0.0724088i	$0.976931\pi$
$774$		0			0
$775$	1.41564	−	11.4763i	0.0508511	−	0.412240i
$776$	1.16362			0.0417715
$777$		0			0
$778$			10.3371i			0.370603i
$779$	3.35026			0.120036
$780$		0			0
$781$	1.25060			0.0447500
$782$			9.40105i			0.336181i
$783$		0			0
$784$	−4.22425			−0.150866
$785$	18.3634	−	16.2374i	0.655419	−	0.579539i
$786$		0			0
$787$			18.2981i			0.652255i	0.945326	+	0.326128i	$0.105744\pi$
$787$			18.2981i			0.652255i	−0.945326	+	0.326128i	$0.894256\pi$
$788$		−	3.87399i		−	0.138005i
$789$		0			0
$790$	−23.9756	+	21.1998i	−0.853012	+	0.754256i
$791$	37.3522			1.32809
$792$		0			0
$793$			2.70052i			0.0958984i
$794$	31.4372			1.11567
$795$		0			0
$796$	3.47627			0.123213
$797$			8.55008i			0.302859i	0.988468	+	0.151430i	$0.0483877\pi$
$797$			8.55008i			0.302859i	−0.988468	+	0.151430i	$0.951612\pi$
$798$		0			0
$799$	31.8496			1.12676
$800$	4.96239	+	0.612127i	0.175447	+	0.0216420i
$801$		0			0
$802$			5.94921i			0.210074i
$803$			5.19791i			0.183430i
$804$		0			0
$805$	6.70052	+	7.57784i	0.236162	+	0.267084i
$806$	−3.12268			−0.109992
$807$		0			0
$808$		−	8.88717i		−	0.312649i
$809$	50.7269			1.78346			0.891731	−	0.452566i	$-0.149491\pi$
$809$	50.7269			1.78346			0.891731	+	0.452566i	$0.149491\pi$
$810$		0			0
$811$	10.3272			0.362638			0.181319	−	0.983424i	$-0.441963\pi$
$811$	10.3272			0.362638			0.181319	+	0.983424i	$0.441963\pi$
$812$		−	12.1016i		−	0.424682i
$813$		0			0
$814$	18.1768			0.637096
$815$	−35.1998	+	31.1246i	−1.23300	+	1.09025i
$816$		0			0
$817$			10.3127i			0.360794i
$818$		−	30.9986i		−	1.08384i
$819$		0			0
$820$	−4.96239	−	5.61213i	−0.173294	−	0.195984i
$821$	−36.5139			−1.27434			−0.637172	−	0.770722i	$-0.719896\pi$
$821$	−36.5139			−1.27434			−0.637172	+	0.770722i	$0.719896\pi$
$822$		0			0
$823$		−	23.0982i		−	0.805154i	−0.915386	−	0.402577i	$-0.868115\pi$
$823$		−	23.0982i		−	0.805154i	0.915386	−	0.402577i	$-0.131885\pi$
$824$	−7.03761			−0.245167
$825$		0			0
$826$	3.47627			0.120955
$827$			3.37470i			0.117350i	0.998277	+	0.0586749i	$0.0186875\pi$
$827$			3.37470i			0.117350i	−0.998277	+	0.0586749i	$0.981312\pi$
$828$		0			0
$829$	−22.6399			−0.786316			−0.393158	−	0.919471i	$-0.628617\pi$
$829$	−22.6399			−0.786316			−0.393158	+	0.919471i	$0.628617\pi$
$830$	16.1260	+	18.2374i	0.559742	+	0.633030i
$831$		0			0
$832$		−	1.35026i		−	0.0468119i
$833$			29.4109i			1.01903i
$834$		0			0
$835$	−16.6253	+	14.7005i	−0.575342	+	0.508733i
$836$	−1.61213			−0.0557566
$837$		0			0
$838$			34.3390i			1.18622i
$839$	−9.02776			−0.311673			−0.155836	−	0.987783i	$-0.549807\pi$
$839$	−9.02776			−0.311673			−0.155836	+	0.987783i	$0.549807\pi$
$840$		0			0
$841$	−15.9525			−0.550088
$842$		−	22.8627i		−	0.787902i
$843$		0			0
$844$	−9.92478			−0.341625
$845$	16.5550	+	18.7226i	0.569509	+	0.644077i
$846$		0			0
$847$		−	28.1457i		−	0.967098i
$848$			11.9248i			0.409499i
$849$		0			0
$850$	4.26187	−	34.5501i	0.146181	−	1.18506i
$851$	15.2243			0.521881
$852$		0			0
$853$			43.1852i			1.47863i	0.673358	+	0.739317i	$0.264851\pi$
$853$			43.1852i			1.47863i	−0.673358	+	0.739317i	$0.735149\pi$
$854$	6.70052			0.229287
$855$		0			0
$856$	0.775746			0.0265145
$857$			33.0249i			1.12811i	0.825737	+	0.564055i	$0.190759\pi$
$857$			33.0249i			1.12811i	−0.825737	+	0.564055i	$0.809241\pi$
$858$		0			0
$859$	−15.1754			−0.517777			−0.258889	−	0.965907i	$-0.583356\pi$
$859$	−15.1754			−0.517777			−0.258889	+	0.965907i	$0.583356\pi$
$860$	17.2750	−	15.2750i	0.589074	−	0.520875i
$861$		0			0
$862$			11.5975i			0.395014i
$863$		−	39.4763i		−	1.34379i	−0.740647	−	0.671894i	$-0.765481\pi$
$863$		−	39.4763i		−	1.34379i	0.740647	−	0.671894i	$-0.234519\pi$
$864$		0			0
$865$	24.4993	−	21.6629i	0.833001	−	0.736561i
$866$	27.8350			0.945871
$867$		0			0
$868$			7.74798i			0.262984i
$869$	−23.0738			−0.782725
$870$		0			0
$871$	13.4010			0.454077
$872$			20.1622i			0.682778i
$873$		0			0
$874$	−1.35026			−0.0456733
$875$	−21.1900	−	30.8872i	−0.716352	−	1.04418i
$876$		0			0
$877$		−	52.5256i		−	1.77366i	−0.462091	−	0.886832i	$-0.652901\pi$
$877$		−	52.5256i		−	1.77366i	0.462091	−	0.886832i	$-0.347099\pi$
$878$		−	38.7875i		−	1.30901i
$879$		0			0
$880$	2.38787	+	2.70052i	0.0804952	+	0.0910346i
$881$	41.8007			1.40830			0.704150	−	0.710051i	$-0.251328\pi$
$881$	41.8007			1.40830			0.704150	+	0.710051i	$0.251328\pi$
$882$		0			0
$883$		−	36.9643i		−	1.24395i	−0.783038	−	0.621974i	$-0.786331\pi$
$883$		−	36.9643i		−	1.24395i	0.783038	−	0.621974i	$-0.213669\pi$
$884$	−9.40105			−0.316191
$885$		0			0
$886$	29.2144			0.981477
$887$			36.0724i			1.21119i	0.795772	+	0.605596i	$0.207065\pi$
$887$			36.0724i			1.21119i	−0.795772	+	0.605596i	$0.792935\pi$
$888$		0			0
$889$	46.0263			1.54367
$890$	−4.31265	+	3.81336i	−0.144560	+	0.127824i
$891$		0			0
$892$		−	7.03761i		−	0.235637i
$893$			4.57452i			0.153080i
$894$		0			0
$895$	17.3865	+	19.6629i	0.581165	+	0.657259i
$896$	−3.35026			−0.111924
$897$		0			0
$898$			20.4993i			0.684070i
$899$	−8.35359			−0.278608
$900$		0			0
$901$	83.0249			2.76596
$902$		−	5.40105i		−	0.179835i
$903$		0			0
$904$	11.1490			0.370811
$905$	31.7889	+	35.9511i	1.05670	+	1.19506i
$906$		0			0
$907$			57.6239i			1.91337i	0.291126	+	0.956685i	$0.405970\pi$
$907$			57.6239i			1.91337i	−0.291126	+	0.956685i	$0.594030\pi$
$908$			14.5501i			0.482861i
$909$		0			0
$910$	−7.57784	+	6.70052i	−0.251203	+	0.222120i
$911$	−30.9234			−1.02454			−0.512268	−	0.858825i	$-0.671195\pi$
$911$	−30.9234			−1.02454			−0.512268	+	0.858825i	$0.671195\pi$
$912$		0			0
$913$			17.5515i			0.580870i
$914$	−6.44851			−0.213298
$915$		0			0
$916$	11.4010			0.376701
$917$		−	18.8021i		−	0.620900i
$918$		0			0
$919$	−33.7743			−1.11411			−0.557056	−	0.830475i	$-0.688069\pi$
$919$	−33.7743			−1.11411			−0.557056	+	0.830475i	$0.688069\pi$
$920$	2.00000	+	2.26187i	0.0659380	+	0.0745715i
$921$		0			0
$922$		−	13.5125i		−	0.445009i
$923$			1.04746i			0.0344776i
$924$		0			0
$925$	−55.9511	−	6.90175i	−1.83966	−	0.226928i
$926$	6.20123			0.203785
$927$		0			0
$928$		−	3.61213i		−	0.118574i
$929$	48.6516			1.59621			0.798104	−	0.602519i	$-0.205836\pi$
$929$	48.6516			1.59621			0.798104	+	0.602519i	$0.205836\pi$
$930$		0			0
$931$	−4.22425			−0.138444
$932$			21.9149i			0.717847i
$933$		0			0
$934$	−16.5599			−0.541857
$935$	18.8021	−	16.6253i	0.614894	−	0.543705i
$936$		0			0
$937$			18.7005i			0.610919i	0.952205	+	0.305460i	$0.0988101\pi$
$937$			18.7005i			0.610919i	−0.952205	+	0.305460i	$0.901190\pi$
$938$		−	33.2506i		−	1.08567i
$939$		0			0
$940$	7.66291	−	6.77575i	0.249937	−	0.221000i
$941$	−38.4142			−1.25227			−0.626134	−	0.779716i	$-0.715364\pi$
$941$	−38.4142			−1.25227			−0.626134	+	0.779716i	$0.715364\pi$
$942$		0			0
$943$		−	4.52373i		−	0.147313i
$944$	1.03761			0.0337714
$945$		0			0
$946$	16.6253			0.540535
$947$			44.0362i			1.43098i	0.698621	+	0.715492i	$0.253797\pi$
$947$			44.0362i			1.43098i	−0.698621	+	0.715492i	$0.746203\pi$
$948$		0			0
$949$	−4.35359			−0.141323
$950$	4.96239	+	0.612127i	0.161001	+	0.0198600i
$951$		0			0
$952$			23.3258i			0.755994i
$953$			38.0724i			1.23329i	0.787243	+	0.616643i	$0.211508\pi$
$953$			38.0724i			1.23329i	−0.787243	+	0.616643i	$0.788492\pi$
$954$		0			0
$955$	31.5125	+	35.6385i	1.01972	+	1.15323i
$956$	13.2750			0.429345
$957$		0			0
$958$			30.5256i			0.986239i
$959$	59.1754			1.91087
$960$		0			0
$961$	−25.6516			−0.827473
$962$			15.2243i			0.490850i
$963$		0			0
$964$	−21.3258			−0.686859
$965$	23.7235	−	20.9770i	0.763688	−	0.675273i
$966$		0			0
$967$		−	42.5256i		−	1.36753i	−0.729701	−	0.683766i	$-0.760341\pi$
$967$		−	42.5256i		−	1.36753i	0.729701	−	0.683766i	$-0.239659\pi$
$968$		−	8.40105i		−	0.270020i
$969$		0			0
$970$	−1.72355	−	1.94921i	−0.0553397	−	0.0625855i
$971$	22.1378			0.710435			0.355217	−	0.934784i	$-0.384407\pi$
$971$	22.1378			0.710435			0.355217	+	0.934784i	$0.384407\pi$
$972$		0			0
$973$		−	35.8496i		−	1.14928i
$974$	2.51388			0.0805499
$975$		0			0
$976$	2.00000			0.0640184
$977$		−	21.7480i		−	0.695780i	−0.937535	−	0.347890i	$-0.886898\pi$
$977$		−	21.7480i		−	0.695780i	0.937535	−	0.347890i	$-0.113102\pi$
$978$		0			0
$979$	−4.15045			−0.132649
$980$	6.25694	+	7.07618i	0.199871	+	0.226040i
$981$		0			0
$982$			1.46168i			0.0466441i
$983$		−	9.04746i		−	0.288569i	−0.989536	−	0.144285i	$-0.953912\pi$
$983$		−	9.04746i		−	0.288569i	0.989536	−	0.144285i	$-0.0460881\pi$
$984$		0			0
$985$	−6.48944	+	5.73813i	−0.206771	+	0.182832i
$986$	−25.1490			−0.800908
$987$		0			0
$988$		−	1.35026i		−	0.0429575i
$989$	13.9248			0.442782
$990$		0			0
$991$	−26.0606			−0.827843			−0.413922	−	0.910313i	$-0.635841\pi$
$991$	−26.0606			−0.827843			−0.413922	+	0.910313i	$0.635841\pi$
$992$			2.31265i			0.0734267i
$993$		0			0
$994$	2.59895			0.0824338
$995$	−5.14903	−	5.82321i	−0.163235	−	0.184608i
$996$		0			0
$997$		−	28.2130i		−	0.893514i	−0.894655	−	0.446757i	$-0.852579\pi$
$997$		−	28.2130i		−	0.893514i	0.894655	−	0.446757i	$-0.147421\pi$
$998$		−	5.55149i		−	0.175729i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.d.e.1369.3		6
3.2	odd	2		570.2.d.d.229.4	yes	6
5.2	odd	4		8550.2.a.cr.1.1		3
5.3	odd	4		8550.2.a.cf.1.3		3
5.4	even	2	inner	1710.2.d.e.1369.6		6
15.2	even	4		2850.2.a.bk.1.1		3
15.8	even	4		2850.2.a.bn.1.3		3
15.14	odd	2		570.2.d.d.229.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.d.d.229.1	✓	6	15.14	odd	2
570.2.d.d.229.4	yes	6	3.2	odd	2
1710.2.d.e.1369.3		6	1.1	even	1	trivial
1710.2.d.e.1369.6		6	5.4	even	2	inner
2850.2.a.bk.1.1		3	15.2	even	4
2850.2.a.bn.1.3		3	15.8	even	4
8550.2.a.cf.1.3		3	5.3	odd	4
8550.2.a.cr.1.1		3	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.48119 + 1.67513i) q^{5} +3.35026i q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.48119 + 1.67513i) q^{5} +3.35026i q^{7} +1.00000i q^{8} +(1.67513 - 1.48119i) q^{10} +1.61213 q^{11} +1.35026i q^{13} +3.35026 q^{14} +1.00000 q^{16} -6.96239i q^{17} +1.00000 q^{19} +(-1.48119 - 1.67513i) q^{20} -1.61213i q^{22} -1.35026i q^{23} +(-0.612127 + 4.96239i) q^{25} +1.35026 q^{26} -3.35026i q^{28} +3.61213 q^{29} -2.31265 q^{31} -1.00000i q^{32} -6.96239 q^{34} +(-5.61213 + 4.96239i) q^{35} +11.2750i q^{37} -1.00000i q^{38} +(-1.67513 + 1.48119i) q^{40} +3.35026 q^{41} +10.3127i q^{43} -1.61213 q^{44} -1.35026 q^{46} +4.57452i q^{47} -4.22425 q^{49} +(4.96239 + 0.612127i) q^{50} -1.35026i q^{52} +11.9248i q^{53} +(2.38787 + 2.70052i) q^{55} -3.35026 q^{56} -3.61213i q^{58} +1.03761 q^{59} +2.00000 q^{61} +2.31265i q^{62} -1.00000 q^{64} +(-2.26187 + 2.00000i) q^{65} -9.92478i q^{67} +6.96239i q^{68} +(4.96239 + 5.61213i) q^{70} +0.775746 q^{71} +3.22425i q^{73} +11.2750 q^{74} -1.00000 q^{76} +5.40105i q^{77} -14.3127 q^{79} +(1.48119 + 1.67513i) q^{80} -3.35026i q^{82} +10.8872i q^{83} +(11.6629 - 10.3127i) q^{85} +10.3127 q^{86} +1.61213i q^{88} -2.57452 q^{89} -4.52373 q^{91} +1.35026i q^{92} +4.57452 q^{94} +(1.48119 + 1.67513i) q^{95} -1.16362i q^{97} +4.22425i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 2 q^{5}+O(q^{10}) \) 6 * q - 6 * q^4 - 2 * q^5	\( 6 q - 6 q^{4} - 2 q^{5} + 8 q^{11} + 6 q^{16} + 6 q^{19} + 2 q^{20} - 2 q^{25} - 12 q^{26} + 20 q^{29} + 28 q^{31} - 20 q^{34} - 32 q^{35} - 8 q^{44} + 12 q^{46} - 22 q^{49} + 8 q^{50} + 16 q^{55} + 28 q^{59} + 12 q^{61} - 6 q^{64} - 32 q^{65} + 8 q^{70} + 8 q^{71} + 4 q^{74} - 6 q^{76} - 44 q^{79} - 2 q^{80} + 8 q^{85} + 20 q^{86} + 8 q^{89} - 64 q^{91} + 4 q^{94} - 2 q^{95}+O(q^{100}) \) 6 * q - 6 * q^4 - 2 * q^5 + 8 * q^11 + 6 * q^16 + 6 * q^19 + 2 * q^20 - 2 * q^25 - 12 * q^26 + 20 * q^29 + 28 * q^31 - 20 * q^34 - 32 * q^35 - 8 * q^44 + 12 * q^46 - 22 * q^49 + 8 * q^50 + 16 * q^55 + 28 * q^59 + 12 * q^61 - 6 * q^64 - 32 * q^65 + 8 * q^70 + 8 * q^71 + 4 * q^74 - 6 * q^76 - 44 * q^79 - 2 * q^80 + 8 * q^85 + 20 * q^86 + 8 * q^89 - 64 * q^91 + 4 * q^94 - 2 * q^95

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